Fixed Points in the Ambient Logic

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. We present an extension of the ambient logic with fixed points operators in the style of the -calculus. We give a simple syntactic condition for the equivalence between minimal and maximal fixpoint formulas and show how to subsume spatial analogues of the usual box and diamond operators. 1

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Available from: Silvano Dal Zilio, Nov 06, 2012
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    ABSTRACT: Spatial logics have been used to describe properties of tree-like structures (Ambient Logic) and in a Hoare style to reason about dynamic updates of heap-like structures (Separation Logic). We integrat this work by analyzing dynamic updates to tree-like structures with pointers (such as XML with identifiers and idrefs). Naíve adaptations of the Ambient Logic are not expressive enough to capture such local updates. Instead we must explicitly reason about arbitrary tree contexts in order to capture updates throughout the tree. We introduce Context Logic, study its proof theory and models, and show how it generalizes Separation Logic and its general theory BI. We use it to reason locally about a small imperative programming language for updating trees, using a Hoare logic in the style of O'Hearn, Reynolds and Yang, and show that weakest preconditions are derivable. We demonstrate the robustness of our approach by using Context Logic to capture the locality of term rewrite systems.
    Proceedings of the 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2005, Long Beach, California, USA, January 12-14, 2005; 01/2005
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    ABSTRACT: The Ambient Calculus is a process calculus where processes may reside within a hierarchy of locations. The purpose of this calculus is to study mobility; to this end, processes can move through the location hierarchy and modify it. Therefore, mobility is seen as the change of spatial configurations over time. In order to describe properties of mobile computations we devise a modal logic, solidly based on the Am- bient Calculus, that can talk about space as well as time. We introduce logical oper- ators that can be used to make assertions about locations and their names, and we study their properties.